The three unknown parameters \(\tau , D_a, D_s\)  are obtained by an optimization procedure that seeks those values for which the model satisfies known constraints for isotropic turbulence, namely \(2\langle \Vert {\mathcal {S}}\Vert ^2\rangle =1/\tau _\eta ^2\) , and the two homogeneity relations due to [1]}, \(\langle {\mathcal {A}}{:\mathcal {A}}\rangle =0\) , \(\langle ({\mathcal {A}}{\cdot \mathcal {A}}){:\mathcal {A}}\rangle =0\) . The values obtained by this procedure are \(\tau =0.1302\tau _\eta \) , \(D_s=0.1014/\tau _\eta ^3\) , and \(D_a=0.0505/\tau _\eta ^3\) .
